WASHINGTON -- For nearly a century, a copper smelter near Butte, Mont., processed ore and released lethal chemicals into the environment, including, according to court records, as much as 62 tons of arsenic and 10 tons of lead each day.

In 1983, a few years after the smelter was shut down, the Environmental Protection Agency designated the 300 square miles surrounding it a Superfund site, requiring the parties responsible for the pollution to take steps to clean it up. The owner of the smelter, the Atlantic Richfield Company, says it has spent more than $450 million to fulfill that obligation.

The Supreme Court heard arguments on Tuesday about whether the company must do more in response to a lawsuit filed by about 100 local residents in state court in Montana. The basic question in the case, Atlantic Richfield Company v. Christian, No. 17-1498, was whether the E.P.A. has to approve the additional remediation efforts sought by the landowners.

Since the agency has not granted approval, the company argued, the Superfund law barred the suit. But the Montana Supreme Court let the case go forward.

''Put simply, the property owners are not asking the court to interfere with the E.P.A.'s plan,'' the court said. ''The property owners are simply asking to be allowed to present their own plan to restore their own private property to a jury of 12 Montanans who will then assess the merits of that plan.''

At the United States Supreme Court, most of the justices seemed to contemplate that the agency should have a decisive role. The alternative, several justices suggested, was administrative chaos with the potential to create additional environmental problems.

Justice Stephen G. Breyer said he was wary of letting ''10,000 juries'' impose ''sometimes conflicting duties and leaving it up to hundreds of different judges to decide.''

Lisa S. Blatt, a lawyer for the company, said the Supreme Court should be wary of undermining the effectiveness of the Superfund law. ''This case involves whether the hundreds of thousands of landowners on Superfund sites can bring state lawsuits to implement their own piecemeal hazardous waste cleanups,'' she said.

''Superfund sites contain extremely hazardous substances -- lead, mercury, plutonium, to name a few,'' Ms. Blatt said. ''Excavation, transportation and disposal of these substances is risky not only to neighbors but the millions of people who live next door to Superfund sites. Whether these risks are worth any benefits should be evaluated by E.P.A., not juries on an ad hoc basis.''

Christopher G. Michel, a lawyer for the federal government arguing in support of the company, said that letting juries ''authorize a plan to clean up toxic contamination at a Superfund site'' would ''jeopardize E.P.A.'s cleanups at this Superfund site and other Superfund sites across the nation.''

But Joseph R. Palmore, a lawyer for the property owners, said the agency's real objection to further remediation was that it was, in bureaucratic jargon, ''technically impracticable.'' That term was a euphemism, he said, for ''too expensive.''

Mr. Palmore also had a broader objection to giving the agency a dominant role. His clients, he said, should not have to seek federal approval to clean up their own property.

''They're saying,'' he said of the company and the agency, ''that my clients in Opportunity, Mont., have to get permission from E.P.A. in Washington if they want to dig out part of their backyard to put in a sandbox for their grandchildren.''

Chief Justice John G. Roberts Jr. said that might be necessary in the circumstances. ''If you want to disturb arsenic-infected land,'' he said, ''you can't overlook the fact that that is going to have harmful effects on everybody else around you.''

Justice Elena Kagan said it would be impractical for the agency to monitor sandbox construction, suggesting that landowners must seek permission first. ''It's hard for E.P.A. to go around and try to figure out who's creating sandboxes,'' she said. ''And so why should the onus be on E.P.A. to figure out who's creating sandboxes?''

Justice Neil M. Gorsuch asked whether the Superfund law amounted to an unconstitutional government taking of private property. Mr. Michel, the lawyer for the federal government, responded that ''it would be a very weak claim given that, in fact, E.P.A.'s remedy has improved the value of the property and that you have to start from the premise that the property is covered with arsenic.''

Mr. Palmore, the landowners' lawyer, urged the justices not to ''give E.P.A. the vast power that it seeks -- the ability to control forever the removal of a shovelful of dirt from a private landowner's backyard.''

Ms. Blatt responded that toxic waste required special rules. ''Arsenic has no half-life,'' she said. ''It always is there. It cannot be destroyed. It doesn't evaporate. So, yeah, they have some restrictions before they move hazardous waste.''